Solve for $x$ : $x^2 - 17x + 72 = 0$
Answer: The coefficient on the $x$ term is $-17$ and the constant term is $72$ , so we need to find two numbers that add up to $-17$ and multiply to $72$ The two numbers $-8$ and $-9$ satisfy both conditions: $ {-8} + {-9} = {-17} $ $ {-8} \times {-9} = {72} $ $(x {-8}) (x {-9}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -8) (x -9) = 0$ $x - 8 = 0$ or $x - 9 = 0$ Thus, $x = 8$ and $x = 9$ are the solutions.